Tourist hat attire for Italy

I'm planning a trip to Italy for Sept. 2006. I want to ensure I don't
dress like a U.S. tourist. One area id hats. I need to wear a hat,
especially if I'm walking or standing under the sun. Wearing the
typical baseball cap is a no-no, I'm assuming.

Anyone have any advice for wearing hats in Italy while sightseeing?

Thank you,

Ed S.

While many would advocate the use of tinfoil for someone like you, in
all practicality aluminum foil is a lot more accessable and would do you
just fine. Nanu nanu.